Question

Solve the given equation and indicate the number of values of θ sach that 0≤θ<2π ,that satisfy the iquation;
Sina=½ 3^½

Answer 1

Is the equation: sin(a) = sqrt(3)/2 ? There are 2 angles that have a positive (sin) of sqrt(3)/2 in the unit circle.

To solve the equation: we use the (sin inverse) functions; they take a number and spit back an angle.

sin(a) = sqrt(3)/2
sin-1(sin(a)) = sin-1(sqrt(3)/2)
a = sin-1(sqrt(3)/2)
a = pi/3

Now the issue here is that sin-1 only gives you an angle between (-pi/2) and (pi/2) so you have to revert back to the original question to ALL the angles.

60 degrees (pi/3) and,

120 degrees (2pi/3)

Does that make sense?

Answer 2

Equation is sina=plus,minus 1/2 sqrt(3)?

Answer 3

If it is sin(a) = +- sqrt(3)/2 then there are 4 angles that we can use; and they all have a reference angle of (60 degrees).

In quadrant 1 we have (pi/3) which is 60 degrees
In quadrant 2 we have (2pi/3) which is 120 degrees
In quadrant 3 we have (4pi/3) which is 240 degrees
In quadrant 4 we have (5pi/3) which is 320 degrees

Answer 4

Make sense.Thank you